Chapter 11, Problem 69GP

Why might tall narrow SUVs and buses be prone to “rollover”? Consider a vehicle rounding a curve of radius R on a flat road. When just on the verge of rollover, its tires on the inside of the curve are about to leave the ground, so the friction and normal force on these two tires are zero. The total normal force on the outside tires is and the total friction force is F_fr. Assume that the vehicle is not skidding.

1. (a) Analysts define a static stability factor SSF = ω/2h, where a vehicle’s “track width” w is the distance between tires on the same axle, and h is the height of the cm above the ground. Show that the critical rollover speed is

   $v_C=\sqrt{Rg\left(\frac{w}{2h}\right)}$

   [Hint: Take torques about an axis through the center of mass of the SUV, parallel to its direction of motion.]

2. (b) Determine the ratio of highway curve radii (minimum possible) for a typical passenger car with SSF = 1.40 and an SUV with SSF = 1.05 at a speed of 90 km/h.